tan27° + tan18° + tan27°. tan18°  = 1

As we know that

tan(A+B) = tanA+tanB/1-tanAtanB

So tan (18+27)=tan18+tan27/1-tan18tan27

1 = tan45=tan18+tan27/1-tan18tan27

as we know tan 45 = 1 so

tan18+tan27+tan18tan27=1

Hence proved